The F-15 was conceived in the late 60's, and the design was influenced by air combat in Vietnam.
Not a multi-role aircraft, the USAF mantra with the Eagle was "not a pound for air to ground".
They wanted, and got, an uncompromised air to air machine, agile, fast, large fuel and AAM capacity for combat persistence. Plus a gun.
All this came at a cost, an expensive aircraft.
So the Lightweight Fighter Programme happened, when it became clear that enough F-15's could never be afforded to replace all those F-4s and F-106's.
Not a favourite with the USAF brass, who resented any threat to their F-15, the F-16 won out in the LWF competition.
The F-16 was designed some years after the F-15, and took advantage of newly available technology, not least Fly-By-Wire.
Originally a cheap fighter, armed with a gun and Sidewinder AAM's, the F-16 of course has demonstrated massive development potential.
The F-16, being smaller the the F-15, and with it's famed agility, is probably better for close in dogfighting. Though the F-15 with it's bigger fuel and missile load, and more powerful radar, is a better interceptor. Both have a good view from the cockpit, the edge here is with the F-16, plus that seat it has to reduce the chance of blacking out during high-G manoevering.
The F-15 hasn't stood still, but the fighter versions at least have not had anything like the upgrading that the F-16 has. But the F-16 has been built in huge numbers, and is a swing-role aircraft.
But both are armed with AMRAAM and Sidewinders, plus the 20mm gun.
I suspect that the F-16 is easier to maintain, hopefully any current or former USAF people on here can verify.
The average age of the USAF F-15 fleet is going to be older than the F-16, and it's a more complex machine.
The F-15E is more modern, for a different mission. It must be heavier than the F-15C, all those pounds for air-to-ground after all.
Of course, a 1984 unmodified vintage F-16C won't be as up to date as a 1991 vintage F-15E. But a European F-16A, recently upgraded under the MLU programme, will be more modern than a slightly newer F-15C.
A few F-15C's have had an electrically-scanned radar fitted, for trials.
As newer versions of the F-16 appear, and the F-15 probably goes out of production, the technology gap between the two will lengthen.

as the newer Blcok 50/52 and improved F-16 CJ come on line with a bigger role in SEAD and as Sandys replacing A-10 the technology will improve. The ability to carry Harm-88s on the CJ is a big plus. The engine flame outs are still a problem but being worked on. Class A mishaps were about the same last year for the Viper as the last few years.

The Eagles are getting old also, and maint is hard. Several maintainers I know say it is ill designed for working on the engines, unlike the F-4 or F-18 which have easier access. The 15 is still the best to plow the road and run CAPs with but Tyndall AFB is getting to take the F-22 as the 15 replacement so plans are underway to slowly transition the Eagle to gaurd duty and maybe even drone work